Finite sphere packing information

finite sphere packing concerns the question of how a finite number of equally-sized spheres can be most efficiently packed. The question of packing finitely...

In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical...

Sphere packing in a sphere is a three-dimensional packing problem with the objective of packing a given number of equal spheres inside a unit sphere. It...

which is homeomorphic to the sphere. The circle packing theorem guarantees the existence of a circle packing with finitely many circles whose intersection...

structures offer the best lattice packing of spheres, and is believed to be the optimal of all packings. With 'simple' sphere packings in three dimensions ('simple'...

defines the translative packing constant of that body. Atomic packing factor Sphere packing List of shapes with known packing constant Groemer, H. (1986)...

block code: it is also known as the sphere-packing bound or the volume bound from an interpretation in terms of packing balls in the Hamming metric into...

this area include: Circle packings Sphere packings Kepler conjecture Quasicrystals Aperiodic tilings Periodic graph Finite subdivision rules Structural...

unit spheres that can be arranged in that space such that they each touch a common unit sphere. For a given sphere packing (arrangement of spheres) in...

lowest maximum packing density of all centrally-symmetric convex plane sets Sphere packing problems, including the density of the densest packing in dimensions...

mathematical theorem about sphere packing in three-dimensional Euclidean space. It states that no arrangement of equally sized spheres filling space has a greater...

Apollonian network, a graph derived from finite subsets of the Apollonian gasket Apollonian sphere packing, a three-dimensional generalization of the...

contributions to group theory, the representation theory of finite groups, the geometry of numbers, sphere packing, and quadratic forms. He is the namesake of Blichfeldt's...

A finite geometry is any geometric system that has only a finite number of points. The familiar Euclidean geometry is not finite, because a Euclidean line...

n-dimensional spheres of a fixed radius in Rn so that no two spheres overlap. Lattice packings are special types of sphere packings where the spheres are centered...

\right)\right)+o\left(1\right)} Block codes are tied to the sphere packing problem which has received some attention over the years. In two dimensions...

touching quadruples (3-simplices) in a sphere packing. The simplicial complex recognition problem is: given a finite simplicial complex, decide whether it...

Hyperplane Lattice Ehrhart polynomial Leech lattice Minkowski's theorem Packing Sphere packing Kepler conjecture Kissing number problem Honeycomb Andreini tessellation...

atomic packing factor (APF). This is calculated by assuming that all the atoms are identical spheres, with a radius large enough that each sphere abuts...

randomly pack in a finite container up to a packing fraction between 75% and 76%. In 2008, Chen was the first to propose a packing of hard, regular tetrahedra...

configuration for the packing of four equal spheres. The dense random packing of hard spheres problem can thus be mapped on the tetrahedral packing problem. It...

conjecture could be carried over to the Euclidean case. Finite Field Kakeya Conjecture: Let F be a finite field, let K ⊆ Fn be a Kakeya set, i.e. for each vector...

polyhedra Conway polynomial (finite fields) – an irreducible polynomial used in finite field theory Conway puzzle – a packing problem invented by Conway...

extreme points. Every graph that can be drawn on a plane can be drawn on the sphere as well, and vice versa, by means of stereographic projection. Plane graphs...

; Sloane, N. J. A. (1988). "Algebraic Constructions for Lattices". Sphere Packings, Lattices and Groups. New York, NY: Springer. doi:10.1007/978-1-4757-2016-7...